The field of optics has been dominated by the study of beam-like fields which obey the transversality condition. However, different manifestations of electromagnetic fields exist where one cannot assign a direction for the net flow of energy. Situations where the electromagnetic fields are essentially three-dimensional occur close to the surface or inside optically inhomogeneous media or in the proximity of radiation sources. Similar circumstances are at the heart of near-field optics and multi-photon microscopies.
In one way or another, all properties of light are exploited as carriers of information. Intensity and wave vectors are at the core of various imaging techniques. The spectral composition of light provides the spectroscopic information characteristic to the intricate interaction between radiation and matter. The state of polarization of optical radiation offers even more insights into phenomena such as light generation and its interaction with material systems. Unfortunately, measuring the detailed characteristics of electromagnetic fields of visible light is a formidable task because it requires discriminating about 10^15 oscillations per second. This is why light fields are usually characterized by average rather than instantaneous properties.
In general, it is considered that light whose electric field oscillates in a particular way is polarized. More specifically, an electric field is said to be polarized if and only if the field vector at a point traces an ellipse with increasing time. The situation is of course idealized; in practice, one encounters electromagnetic fields which are not perfectly harmonic but rather fluctuating quantities. This happens because light is usually generated by a large number of random atomic oscillators. Their emissions combine momentarily to form a polarized wave, but this will persist only for a very short time before different atomic oscillators emit new randomly polarized waves causing a different polarization of the resultant superposition. Consequently, the polarization of light fluctuates too rapidly to be detectable, a situation which is called random polarization. In many cases, the electromagnetic fields are neither fully polarized nor completely random or, in other words, the light is partially polarized as described in J. Ellis and A. Dogariu, “On the degree of polarization of random electromagnetic fields”, Optics Communications, Vol. 253, (15 Sep. 2005) pp. 257-265, and describing these properties of electromagnetic fields constitutes the aim of polarimetry.
The polarization properties of light have been researched for more than 300 years and there is a plethora of experimental methods for determining the correlations between orthogonal components of the electric field, and from these, the conventional polarimetric parameters.
Traditionally, this was limited to beam-like fields where the electric field vector fluctuates in a plane perpendicular to the direction of propagation. However, electromagnetic fields can also be three-dimensionally structured. Such field manifestations occur in the study of multiple light scattering, in the proximity of radiation sources, or in various situations pertinent to near-field optics and multiphoton microscopies. So far, determining directly the properties of three-dimensional fields was not possible and one had to rely on measurements performed far from the source and then relate these to the properties of the field of interest. While the direct problem of calculating the properties of the far-field for a given source can be straightforward, the inverse problem—which is usually of interest in practice—does not have a unique solution. Progress in solving the inverse problem can be achieved only by either making assumptions regarding the properties of the field to be determined or by performing additional measurements along different directions of propagation. Nevertheless, having direct access to the three-dimensional field would be a better option!
The complete determination of the characteristics of a three-dimensional field requires simultaneous measurements of the properties of the field in three different directions. This is realized by using three orthogonal dipole-like probes which are overlapped spatially and which are detected simultaneously. In the optical domain however, this approach cannot be implemented because an ensemble of three dipoles which can be read independently simply does not exist.
Instead of superposing three dipole-like detectors, the device, system and method of the present invention uses a probe that is placed within the three-dimensional field. The probe couples all three components of the field and then re-emits the radiation. The probe acts a secondary source for the radiation which will eventually be sensed by a conventional detector placed away from the point of measurement. The result is a linear combination of the measurements possible with three independent dipoles. In order to determine the entire polarimetric information, measurements are performed with multiple probes. Different probe designs can be implemented.
The apparatus, system and method of the present invention provide a novel approach for characterizing the polarization properties of electromagnetic fields which fluctuate three-dimensionally. The state of polarization of an optical field provides detailed information concerning both the radiation emission processes and the intricate interaction between light and matter. Using probes which couple all three components of the field, the polarized and unpolarized components of such fields are extracted to produce what could be called “three-dimensional polarimetry”.